Bandwidth of One Pole

A typical formula relating 3-dB bandwidth (in Hz) to the pole radius $R\in[0,1)$ is

$\displaystyle \zbox {R = e^{- \pi B T}} \protect$

(9.7)

where

denotes the sampling interval as usual. Solving for

gives

$\displaystyle B = - \frac{\ln(R)}{\pi T}.$

In §E.6 (see also §B.1.3), it is shown that

is the 3-dB bandwidth or half-power bandwidth, in the limit, as the sampling rate goes to infinity.

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Time Constant of One Pole
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Stability Revisited

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